(1) Field of the Invention
This invention relates to pneumatic structures, and more particularly to such structures wherein a membrane is supported by fluid pressure thereunder.
(2) Description of the Prior Art
Before this application was filed, a search was made in the U.S. Patent and Trademark Office. That search developed the following U.S. Pat. Nos.:
______________________________________ SUITS 2,649,101 LINGAFELTER 2,920,846 DEMARTEAU 3,123,085 NEUMARK 3,169,542 LAING 3,249,682 MEYER ET AL 3,373,531 CAPLAN 3,475,915 McCONNELL ET AL 3,480,023 SCHNEIDLER 3,626,836 SINOSKI 3,740,902 KOLIOMICHALIS 3,747,131 AMARANTOS 3,999,333 KWAKE 4,004,380 PITTMAN 4,176,653 ______________________________________
These patents are considered pertinent because the applicant believes the Examiner would consider anything returned by the searcher to be relevant and pertinent to the examination of this application. The applicant is also aware of the following specific reference on pneumatic structures (hereinafter referred to as Otto.): Tensile Structures, edited by Frei Otto, The MIT Press, Cambridge, Mass. (1973); Library of Congress catalog card number: 73-3123. Applicant believes that The MIT Press has published an updated version of this reference, although applicant is unaware of its contents or identity.
In the pneumatic structure to which this invention relates, a membrane is connected at its periphery to a foundation. Otto calls the pliant covering a membrane and so will applicant, meaning by this term a fluid-tight, flexible sheet of material which separates the fluid above from the fluid below. It will be understood the foundation may or may not include walls and other superstructures, as desired, the term foundation being defined as structure connecting the membrane periphery to the ground to form a substantially fluid-tight enclosure. The term "periphery" refers to the boundary of the membrane, where the membrane is connected to the foundation or a rigid structural part thereof, such that substantial movement of the membrane at the point of connection is prevented. The membrane is supported by an internal fluid pressure greater than the external fluid pressure. This pressure differential exerts a uniform force on the membrane surface, which causes the membrane to assume a dome shape. The term "dome" means that at least one area of the membrane is elevated above other areas of the membrane. According to Otto, pages 10-17, the cross-section of the dome will be arcuate, approximating a segment of a circle, because this shape results in the least membrane stress.
For illustrative purposes, the shape of the dome of this application will be assumed herein to be a longitudinal section of a cylinder, similar to that schematically represented in FIG. 8, although it will be understood that the fundamental principles illustrated herein apply to any other membrane shape. Referring to FIG. 9, the arcuate cross-section of the dome taken perpendicularly to the axis of the cylinder has a curvature c,1 and a radius of curvature r,1. Otto, pages 70-77 reveals that the tangential stress within the membrane at any point on the arcuate cross-section will be approximated by the function: s=(p).times.(r), where: s=tangential stress at any point on the membrane; p=differential pressure=internal fluid pressure-external fluid pressure; r=radius of curvature of the arcuate cross-section. As the radius of curvature increases, the stress increases. This relationship between stress, radius of curvature and pressure differential holds true for other membrane shapes, although the function describing the relation of r and p to s may vary for different membrane shapes (Otto, pages 10-17, 78-109).
Recalling the formula s=(p).times.(r), for a given constant pressure (p) sufficient to support the membrane, the arcuate cross-section defined by the curvature c,1 and radius of curvature r,1 in FIG. 9, where r,1=1/2 the building width, is the arcuate cross-section having the least membrane stress, since r,1 represents the minimum possible radius for a single dome (Otto, p.31). The height of this dome is also 1/2 the building width. This dome has a large volume under the membrane, which requires much greater heating and cooling capacity than a conventionally constructed building or flatter membrane shape. The membrane height appears out of proportion to the building width. The surface of the dome could be more subject to deflection and oscillation by wind forces than a flatter membrane shape. The quantity of membrane fabric required is greater than for a flatter membrane shape.
Others have recognized the desirability of a flattened membrane. Some have used tension structures connecting points on the membrane with the ground or foundation to flatten the membrane. DEMARTEAU employs a net covering the membrane, with the net being secured to the walls and foundation by an elaborate network of tension cables. Similarly, NEUMARK employs tension cables connecting points on the membrane to the ground. MEYER ET AL pass a single tension cable over the membrane connected to the ground, as schematically shown in FIG. 9 by curvature c,2 radius r,2 and cables t. MEYER ET AL use a rigid tube to maintain a flat depression, since without the rigid tube the cable and membrane would define an arc. PITTMAN creates dimples in the membrane surface by connecting areas of the membrane to rigid ground supported frames. This prior art teaches the use of tension connections of the membrane surface to the ground or foundation to hold areas of the membrane down, i.e., to prevent areas of the membrane from going up. This prior art accomplishes several benefits in addition to flattening the membrane. Again referring to FIG. 9, it may be seen that several smaller domes may be created with tension cables t, shown as curvatures c,2 and radii of curvature r,2. The radius of curvature r,1, as taught by MEYER ET AL and substantially by NEUMARK, has been reduced to r,2 thereby reducing the membrane stress. Additionally, the tension exerted by the membrane on the foundation at the membrane periphery is reduced, and shared by the tension cables t connecting the depressed areas of the membrane to the ground or foundation.
Others, such as SINOSKI, have flattened the membrane by simply decreasing the membrane area, and thereby increasing the radius of curvature of the single membrane dome, as schematically reflected in FIG. (10). The increase from radius of curvature r,1 to r,3 results in a corresponding increase in membrane stress. SINOSKI employs expansion joints and extraordinarily strong membrane material, such as steel, to account for this increased membrane stress.
Although previous work in the art solved some problems in reducing membrane height and in some cases reducing membrane stress, several problems remained unsolved prior to this invention. FIG. 11 schematically shows the force exerted on a cylindrical membrane structure having the membrane periphery near the ground during wind conditions, where the length of the vectors indicates amount of force. The area of the membrane close to the ground will be subjected to substantial positive (+) wind loads. It is therefor necessary to maintain sufficient pressure differential (p) and therefor sufficient membrane stress (s) to resist deflection or buckling of the membrane near the ground. For example, a 60 mph surface wind will subject the lower membrane surface, or wall, of a building according to the MEYER ET AL and NEUMARK prior art to approximately 0.05 psi positive pressure. Therefore, a pressure differential of at least 0.05 psi would be necessary to prevent buckling of the membrane wall during a 60 mph wind.
Increased pressure to cure the above problem exacerbates another problem. The membrane area above the ground is simultaneously subjected to negative (-) wind loads. The prior art teaches that inflatable buildings must assume the maximum volume shape. No significant vertical movement of the membrane is permitted in the prior art design to expand the volume of the structure. Therefore, any negative pressure at the top of the membrane is transmitted directly to the fabric as lift, or vacuum, externally, while the internal pressure remains constant because the volume of the building is unchanged. The decreased external pressure at the roof top increases the pressure differential (p), at that area of the membrane, and hence increases the membrane stress (s). A prior art building with 0.05 psi differential pressure will have uniform stress throughout the membrane for the static case with no wind loads. For the 60 mph wind example, some areas of the membrane at the top of the building will be subjected to a negative pressure or vacuum of 0.15 psi as the wind passes over the building. The internal pressure differential of 0.05 psi is added to the negative pressure of 0.15 psi, and a total pressure differential of 0.20 psi is exerted on areas of the membrane during 60 mph winds. This is a fourfold increase in membrane stress from the static case. When the wind speed exceeds the speed at which the positive dynamic pressure exerted on the walls equals the differential pressure, (for the example, greater than 60 mph), the prior art building will indent at the leading edge near the ground, as shown in FIG. 11. This distortion will increase the internal pressure because the indentation lessens internal volume. The negative pressure, or vacuum at the top of the building will also be correspondingly greater for greater wind speeds, increasing differential pressure at some areas of the membrane manyfold and deforming the structure as further shown in FIG. 11. The fabric stress has now risen drastically. This stress increasing phenomenon is one primary design problem associated with the prior art.
If the membrane periphery is connected to the top of building walls as shown by SINOSKI, the walls will absorb some positive wind loads. However, the upper portions of the membrane will still be subjected to negative wind loads, with the attendant problems cited above, because the prior art designs do not permit significant upward movement of the membrane to adequately respond to wind load conditions.
Additionally, with the prior art, the membrane height, and the amount of fluid in the structure, could not be conveniently varied without substantially changing internal pressure. The cost, size, complexity and difficulty of installation and maintenance of cable systems increases with the area to be spanned. Internal cable systems might interfere with efficient use of the building.